Circularity of the STFT and spectral kurtosis for time-frequency segmentation in white Gaussian environment

This paper investigate the circularity of Short Time Fourier Transform (STFT) coefficients noise only, and proposes a modified STFT such that all coefficients coming from white Gaussian noise are circular. In order to make use of the spectral kurtosis (SK) for a stop criterion, we consider the spectral kurtosis of circular random variables, and its link with the kurtosis of the real and imaginary part, and show that the variance of the SK is smaller than the variance of the kurtosis estimated from both real and imaginary parts. The effect of the non-circularity of Gaussian variables upon the spectral kurtosis of STFT coefficients is studied, as well as the effect of signal presence. Finally, a time-frequency segmentation algorithm based on successive iterations of noise variance estimation and time-frequency coefficients detection is proposed. The iterations are stopped when the spectral kurtosis on non-detected points reaches zero. Examples of segmented time-frequency space are presented on a dolphin whistle and on a simulated signal in non-white and non-stationary Gaussian noise. Index Terms Short time Fourier transform, circularity, spectral kurtosis, time-frequency segmentation, statistical segmentation, time-frequency analysis EDICS: SSP-NSSP